Introduction In the simplest model of a telephone speech communication there is a direct, dedicated, physical connection between the two participants in the conversation, and this link is held for the duration of the conversation. The analogue electrical signal produced by the telephone at either end is sent on to connection without modification. In Pulse Amplitude Modulation (PAM), the unmodified electrical signal is not sent on to the connection. Instead, short samples of the signal are taken at regular intervals, and these samples are sent on to the connection. The amplitude of each sample is identical to the signal voltage at the time when the sample was taken. Typically, 8,000 samples are taken per second, so that the interval between samples is 125s, and the duration of each sample is approximately 4s. Because each sample is very short (~4s) there is a lot of time between samples (~121s). Samples from other conversations are put into this “spare time”. Usually the samples from 32 separate conversations are put on to a single line. This process is called Time Division Multiplexing (TDM). Each sample is very short, and will be distorted as it travels across a communications network. In order to reconstruct the original analogue signal the only information the receiver needs to have about a sample is its amplitude, but if this is distorted then all information about the sample has been lost. To overcome this problem, the pulse is not transmitted directly, instead its amplitude is measured and converted into an 8 binary number - a sequence of 1s and 0s. At the receiver end, the receiver merely needs to detect if a 1 or a 0 has been received so that it can still recover the amplitude of a PAM pulse even if the 1s and 0s used to describe it have been distorted. The process of converting the amplitude of each pulse into a stream of 1s and 0s is called Pulse Code Modulation (PCM) Note that the process of PAM and PCM (but without the use of TDM) is essentially used to store music and speech on CDs, but with a higher sample rate, more bits per sample and complex error correction mechanisms. Some terms are: Sampling The process of measuring the amplitude of a continuous-time signal at discrete instants. It converts a continuous-time signal to a discrete-time signal. Quantizing Representing the sampled values of the amplitude by a finite set of levels. It converts a continuous-amplitude sample to a discrete-amplitude sample. Encoding Designating each quantized level by a (binary) code. Sampling and quantizing operations transform an analogue signal to a digital signal. Use of quantizing and encoding distinguishes PCM from analogue pulse modulation methods. The quantizing and encoding operations are usually performed in the same circuit at the transmitter, which is called an Analogue to Digital Converter (ADC). At the receiver end the decoding operation converts the (8 bit) binary representation of the pulse back into an analogue voltage in a Digital to Analogue Converter (DAC) 1 28/06/2016 1. Time Division Multiplexing (TDM) - Principle When sending samples of a signal instead of the signal itself there is time available between each of the samples. Samples from other analogue signals can be put into this space. The process of splitting up the Receiver Transmitter time into slots and putting Timing Timing different signals into the time slots is known as Time Ch1 Ch1 Buffer LPF1 i/p o/p Division Multiplexing Transmission Line Ch1 Ch1 (TDM). A basic real TDM Buffer LPF2 i/p o/p SW1 SW2 Ch1 Ch1 system interleaves 32 Buffer LPF3 i/p o/p signals and uses electronic switches. This is a diagram of a 3 channel PAM-TDM system. This diagram shows the waveforms produced during the operation of the PAM-TDM system The switches connect the transmitter and the receiver to each of the channels in turn for a specific interval of time. In effect each channel is Ch1 sampled and the sample is transmitted When the switches are in the channel 1 position, channel 1 forms a PAM channel with an LPF for Ch2 reconstruction, and so on for channels 2 and 3. The result is that the amplitudes samples from each channel share the line sequentially, becoming interleaved to Ch3 form a complex PAM wave, as shown above. A major problems in any TDM system is the synchronisation of the transmitter and receiver TDM timing circuits. The transmitter and receiver must Signal switch at the same time and frequency. Also SW1 must Guard Slots be in the channel 1 position when SW2 is in the channel Time 1 position, so that the switches must be synchronised in Slots 1 2 3 1 2 3 1 2 3 position also. In a system that uses analogue modulation (PAM) the time slots are separated by guard slots to prevent crosstalk between channels. 2 28/06/2016 2. Sampling Theorem Consider a band-limited signal with no frequency components above a certain frequency fm. The sampling theorem states that this signal can be recovered completely from a set of samples of its amplitude, if the samples are taken at the rate of fs > 2fm samples per second. This is often called the uniform sampling theorem for baseband or low-pass signals. The minimum sampling rate, 2fm samples per second, is called the Nyquist sampling rate (or Nyquist frequency); its reciprocal l/(2fm) (measured in seconds) is called the Nyquist interval. fs = 2 * fm is called the Nyquist sampling rate. For telephone speech the standard sampling rate is 8 kHz (or one sample every 125 s). 2.1 Sampling Methods Suppose we have an arbitrary signal (the baseband signal m(t)) which has a spectrum M(f). Take infinitesimally short samples of the Freq signal m(t) at a uniform rate once Sampling pulses fs 2fs 3fs every ts seconds i.e. at a frequency fs. This is the ideal form of sampling, it is Spectrum of Sampling Pulses Spacing = 1/fs called instantaneous (or impulse) sampling. Samples fs 2fs 3fs In effect the signal m(t) is multiplied by a train of impulses giving rise to a Time train of pulses as in the lower line of Spectrum of Sampled Signal the diagram. The train of sampling impulses has a frequency spectrum consisting of all harmonics or multiples of f s and all are at the same amplitude. This sampled signal has a spectrum as shown where M(f) is repeated unattenuated periodically and appears around all multiples of the sampling frequency (fs = 1/ts). To recover m(t) from the sampled signal we need only pass the sampled signal through a low pass filter with a stop frequency of fs/2. All of the higher frequency components will be dropped. In the diagram, if fs is greater than twice the highest frequency in m(t) the repetitions of the sampled spectra around the harmonics of the fs do not overlap. Signal(mt) Spectrum of Unsampled Signal M(f) 2.1.1 Flat - top Sampling An Analogue to Digital Converter requires that the sample value be held constant for a fixed time until the conversion is completed. This requires a flat-top sampled signal. This has approximately the same repeated frequency spectrum as with the instantaneous sampling above, but with each repetition slightly spread out. The simplest and most common sampling method is performed by a functional block termed a Sample and Hold (S/H) circuit. The output from the circuit must be held at a constant level for the sampling duration. Vcontrol switches the MOSFET ON until the charge on C Input signal is equal to the amplitude of the sampled voltage. + Sample Vcontrol then goes LOW, the MOSFET is OFF Out and the charge is held by the capacitor. The charge held on the capacitor puts a voltage across Vcontrol Gnd the capacitor, and it is held at that value until the next time that Vcontrol switches the MOSFET ON. This is called a sample and hold circuit and is usually used as the input to an ADC. 3 28/06/2016 2.2 Aliasing Error If a signal is under sampled (sampled at a rate below the Nyquist rate), the spectrum consists of overlapping repetitions of the sampled spectrum. Because of the overlapping tails a single repetition of the spectrum no Spectrum of Sampled Signal longer has the complete information about the unsampled signal, and it is no longer possible to recover it from the sampled signal. To recover the original signal at the receiving end the sampled signal is passed through a lowpass filter with a cut off of fs/2, we get a spectrum that is not the sampled signal but is a different version due to: Loss of the tail of the sampled signal spectrum beyond fs/2 This same tail appears inverted, or folded, onto the spectrum at the cut-off frequency. This tail inversion is known as aliasing, (or spectral folding or foldover distortion). The aliasing distortion can be eliminated by cutting the tail (i.e. filtering) of the sampled signal beyond f > fs/2 before the signal is sampled. By so doing, the overlap of successive cycles in the sampled signal is avoided. The only error in the recovery of the unsampled signal is that caused by the missing tail above fs/2. It is simpler to consider aliasing by considering fm fs 2fs 3fs a single frequency component of m(t). We will look at the frequency fm and it is sampled at a rate fs. The diagrams show the frequencies fs-fm fs+fm 2fs-fm 2fs+fm 3fs-fm 3fs+fm which will be present in the sampled signal. There will be frequency components at fm, fs - fm, fs + fm, 2 fs - fm, 2 fs + fm, 3 fs - fm, 3 fs + fm, etc. etc. In the first case fm is very much less than fs, so fm that fs - fm is much higher than the cut off of the filter (fs/2). In the second case fm is below, but close to fs/2, fs-fm fs+fm 2fs-fm 2fs+fm 3fs-fm 3fs+fm so that a sharp cut off filter is required to ensure that fm is passed but fs - fm is stopped. In the third case fm is higher than fs/2, so that fs - fm is less than fs/2. The low pass filter with a cutoff of fs/2 will therefore block fm (the actual fm signal frequency) but will pass a signal with frequency fs - fm. This is aliasing fs-fm 2fs-fm fs+fm 3fs-fm 2fs+fm 3fs+fm Strictly speaking, a band limited signal does not exist in reality. It can be shown that if a signal is time limited it cannot be band limited. All Frequency physical signals are necessarily time limited because they begin at some finite instant and must terminate at some other finite instant. Hence, all practical signals are theoretically non band limited. A real signal contains a finite amount of energy, therefore its frequency spectrum must decay at higher frequencies. Most of the signal energy resides in a finite band, and the spectrum at higher frequencies contributes little. The error introduced by cutting off the tail beyond a certain frequency B can be made negligible by making B sufficiently large. Thus, for all practical purposes a signal can be considered to be essentially band limited at some value B, the choice of which depends upon the accuracy desired. A practical example of this is a speech signal. Theoretically, a speech signal, being a finite time signal, has an infinite bandwidth. But frequency components beyond 3400 Hz contribute a small fraction of the total energy. When speech signals are transmitted by PCM they are first passed through a lowpass filter of bandwidth of 3500 Hz. (This filter is called an anti aliasing filter). Higher sampling rates (i.e. 8000 samples/sec) permits recovery of the signal from its samples using 4 28/06/2016 relatively simple filters i.e. it allows for guard bands between the repetitions of the spectrum (otherwise recovering signals sampled at the Nyquist rate would require very sharp cut-off (ideal) filters). In summary, aliasing distortion produces frequency components in the desired frequency band that did not exist in the original waveform. Aliasing problems are not confined to speech digitisation processes. The potential for aliasing is present in any sample data system. Motion picture taking, for example, is another sampling system that can produce aliasing. A common example occurs when filming a rotating wheel. Often the sampling process (the picture refresh rate) is too slow to keep up with the wheel movements and spurious rotational rates are produced. If the wheel rotates 3550 between frames, it looks to the eye as if it has moved backwards 50. 3. Pulse Amplitude Modulation A sampled signal consists of a train of pulses, where each pulse corresponds to the amplitude of the signal at the Input Transmission corresponding sampling time. The Signal Band Limiting Sampling Link Sample LPF Filter Circuit and Hold signal sent to line is modulated in amplitude and hence the name Pulse Sampling Pulses Amplitude Modulation (PAM). A complete PAM system must include a band limiting (or anti aliasing) filter before sampling to ensure that no spurious or source-related signals get folded back into the desired signal bandwidth - no aliasing. The input filter may also be designed to cut off very low frequencies to removed 50 Hz hum from power lines. Several PAM signals can be multiplexed together as long as they are kept distinct and are recoverable at the receiving end. This system is one example of Time Division Multiplex (TDM) transmission (although it has never been widely used fo speech, it has applications in remote monitoring and telemetry). The sample-and-hold circuit takes in each pulse and holds the amplitude of that pulse until the arrival of the next pulse. It produces a staircase approximation to the sampled wave form. With use of the staircase approximation, the power level of the signal coming out of the reconstructive filter (LPF) is nearly the same as the level of the sampled input signal. The filters are assumed to have ideal characteristics - not like real filters. Filters with real attenuation slopes at the band edge can be used if the input signal is slightly over sampled. If sampling frequency is greater than twice the bandwidth, the spectral bands are sufficiently separated from each other that filters with gradual roll-off characteristics can be used. As an example, sampled voice systems typically use band limiting filters with a 3 dB cut-off around 3.4 kHz and a sampling rate of 8 kHz. Thus the sampled signal is sufficiently attenuated at of 4 kHz to adequately reduce the energy level of the foldover spectrum. 5 28/06/2016 4. Pulse Code Modulation Pulse Code Modulation (PCM) is an extension of PAM wherein each analogue sample value is quantized into a discrete value for representation as a digital code word. Thus, as shown below, a PAM system can be converted into a PCM system by adding a suitable analogue-to-digital (A/D) converter at the source and a digital-to-analogue (D/A) converter at the destination. PCM is a true digital process Modulator as compared to PAM. In Analogue PCM PCM the speech signal is Parallel Digital Input Output A to D Binary Sampler to Serial Pulse converted from analogue to Converter Coder Converter Generator digital form. PCM is standardised for Demodulator telephony by the ITU-T PCM Analogue (International Serial to Input D to A Output LPF Parallel Telecommunications Union Converter Converter Telecoms, a branch of the UN), in a series of recommendations called the G series. For example the ITU-T recommendations for out-ofband signal rejection in PCM voice coders require that 14 dB of attenuation is provided at 4 kHz. Also, the ITU-T transmission quality specification for telephony terminals require that the frequency response of the handset microphone has a sharp roll-off from 3.4 kHz. In quantization the levels are assigned a binary codeword. All sample values falling between two quantization levels are considered to be located at the centre of the quantization interval. In this manner the quantization process introduces a certain amount of error or distortion into the signal samples. This error known as quantization noise, is minimised by establishing a large number of small quantization intervals. Of course, as the number of quantization intervals increase, so must the number or bits increase to uniquely identify the quantization intervals. For example, if an analogue voltage level is to be converted to a digital system with 8 discrete levels or quantization steps three bits are required. In the ITU-T version there are 256 quantization steps, 128 positive and 128 negative, requiring 8 bits. A positive level is represented by having bit 8 (MSB) at 0, and for a negative level the MSB is 1. 4.1 Quantization This is the process of setting the sample amplitude, which can be continuously variable to a discrete value. Look at Uniform Quantization first, where the discrete values are evenly spaced. Output 4.1.1 Uniform Quantization -mp +mp Input We assume that the amplitude of the signal m(t) is confined to the range (-mp, +mp ). This range (2mp) is divided into L levels, each of step size , given by = 2 mp / L A sample amplitude value is approximated by the midpoint of the interval in which it lies. The input/output characteristics of a uniform quantizer is shown. 6 28/06/2016 4.2 Companding In a uniform or linear PCM system the size of every quantization interval is determined by the SQR requirement of the lowest signal to be encoded. This interval is also for the largest signal - which therefore has a much better SQR. Example: A 26 dB SQR for small signals and a 30 dB dynamic range produces a 56 dB SQR for the maximum amplitude signal. In this way a uniform PCM system provides unneeded quality for large signals. In speech the max amplitude signals are the least likely to occur. The code space in a uniform PCM system is very inefficiently utilised. A more efficient coding is achieved if the quantization intervals increase with the sample value. When the quantization interval is directly proportional to the sample value ( assign small quantization intervals to small signals and large intervals to large signals) the SQR is constant for all signal levels. With this technique fewer bits per sample are required to provide a specified SQR for small signals and an adequate dynamic range for large signals (but still with the SQR as for the small signals). The quantization intervals are not constant and there will be a non linear relationship between the code words and the values they represent. compressed signal level Originally to produce the non linear quantization the baseband signal was passed through a non-linear amplifier with input/output characteristics as shown input signal level before the samples were taken. Low level signals were amplified and high level signals were attenuated. The larger the sample value the more it is compressed before encoding. The PCM decoder expands the compressed value using an inverse compression characteristic to recover the original sample value. The two processes are called companding. There are 2 companding schemes to describe the curve above: 1. -Law Companding (also called log-PCM) This is used in North America and Japan. It uses a logarithmic compression curve which is ideal in the sense that quantization intervals and hence quantization noise is directly proportional to signal level (and so a constant SQR). 2. A- Law Companding This is the ITU-T standard. It is used in Europe and most of the rest of the world. It is very similar to the -Law coding. It is represented by straight line segments to facilitate digital companding. Originally the non linear function was obtained using non linear devices such as special diodes. These days in a PCM system the A to D and D to A converters (ADC and DAC) include a companding function. 4.3 PCM Encoding Process (HDB3) The output from the analogue to digital converter (ADC) has n parallel bits. In the case of telephony n = 8. The most significant bit is the signed bit. If the measured sample is positive then the signed bit is 0. If the measured sample is negative then the signed bit is 1. The remaining 7 bits are used to code the sample value. The ITU-T define a look up table which allocates a particular binary code to each quantified A-law value. The line coding which is used assigns opposite polarities to successive “1”s. This eliminates any DC voltage on the line, and reduces the inter symbol interference if adjacent bits are “1”. 7 28/06/2016 If there is silence on the PCM channel then the measured samples will be 0 Vrms and the output of the DAC will be 1000 0000. A stream of all zeros is not desirable on an active channel because all zeros could also be a fault condition and it is difficult to recover the clock signal from the incoming signal. The coding system HDB3 is used and was developed to eliminate all zeros, and to assign opposite polarities to successive “1”s. This is a bipolar signalling technique (i.e. relies on the transmission of both positive and negative pulses). In AMI positive and negative pulses (of equal amplitude) are used for alternative symbols 1. No pulse is used for symbol 0. In either case the pulse returns to 0 before the end of the bit interval. This eliminates any DC on the line. HDB3 encoding rules follow those for AMI, except that a sequence of four consecutive 0's are encoded using a special "violation" bit. The 4th 0 bit is given the same polarity as the last 1-bit which was sent using the AMI encoding rule. This prevents long runs of 0's in the data stream which may otherwise prevent a receiver from tracking the centre of each bit. By introducing violations, extra "edges" are introduced, enabling a Digital PLL to reliably reconstruct the clock signal at the receiver. The HDB3 is transparent to the sequence of bits being transmitted (i.e. whatever data is sent, the Digital PLL can reconstruct the data and extract the bits at the receiver). To prevent a DC being introduced by excessive runs of zeros any run of more than four zeros encodes as B00V. The value of B is assigned + or - alternately throughout the bit stream. Example 1111 1111 = + - + - + - + B B B B B B B B 1010 1010 = + 0 - 0 + 0 - 0 B 0 B 0 B 0 B 0 1000 0001 1000 0110 = + 0 0 0 + 00 B 0 0 0 V 00B = = + 0 0 0 + - +0 B 0 0 0 V BB0 4.4 PCM Timing and Synchronisation The PCM receiver must be able to identify the start and finish of each full sampling sequence and to identify each bit position. The sampling clock needs to be either sent to, or regenerated at, the receiving side to determine when each full sequence of sampling begins and ends. The data clock is also needed to determine exactly when to read each bit of information. A PCM channel is sampled at 8,000 Hz or once every 125 s. If there is one channel or 30 TDM channels the sampling period is fixed at 125 data clock 64 kbit/s 15.625 s s and this period is known as a frame. Therefore the frame clock must have a period of 125 s. The rising edge of the frame clock informs the receiver frame clock 125 s that the next bit will be Bit 1 of a new sample. The falling edge of the data clock informs the receiver that it must read the data bit. When the bit stream is transmitted along a line B1 B2 B3 B4 B5 B6 B7 B8 B1 the pulses become distorted and the rise and fall 1 0 1 0 0 1 1 1 ? times become significant. Ideally, a 1 will be “high” 8 28/06/2016 for 15.625 s. In practice the pulse may only be above the “high” threshold for a few s so it is very important that the bit is read within a certain time limit of the clock pulse. The simplest way to synchronise a PCM sender to a PCM receiver is to send the clock signals on different circuits to the data This would be done in a self-contained system such as private branch exchange (PBX). Telephony is full duplex so that there is a coder and a decoder at each port, but each would use the same clock. To minimise the number of circuits it is possible to use a line-coding scheme which allows the receiver to extract the clocks from the PCM signal. In this case the receiver will have free running clocks that lock (using a PLL) to the phase and frequency of the transitions in the data stream. The line-coding scheme ensures that there is a transition for every data bit. 9 28/06/2016 5. Differential pulse coding schemes PCM transmits the absolute value of the signal for each frame. Instead we can transmit information about the difference between each sample. The two main differential coding schemes are: Delta Modulation Differential PCM and Adaptive Differential PCM (ADPCM) 5.1 Delta Modulation Delta modulation converts an analogue signal, normally voice, into a digital signal. The analogue signal is sampled as in the PCM granular noise process. Then the sample is compared with 1 1 the previous sample. The result of the 1 comparison is quantified using a one bit coder. 1 0 0 1 If the sample is greater than the previous 0 1 1 sample a 1 is generated. Otherwise a 0 is 0 0 1 0 0 0 generated. The advantage of delta modulation 0 over PCM is its simplicity and lower cost. But the noise performance is not as good as PCM. To reconstruct the original from the quantization, if a 1 is received the signal is increased by a step of size q, if a 0 is received the output is reduced by the same size step. Slope overload occurs when the encoded waveform is more than a step size away from the input signal. This condition happens when the rate of change of the input exceeds the maximum change that can be generated by the output. Overload will occur if: dx(t)/dt q /T = q * fs where: x(t) = input signal, q = step size, T = period between samples, f s = sampling frequency Assume that the input signal has maximum amplitude A and maximum frequency F. The most rapidly changing input is provided by x(t) = A * sin (2 * * F * t). For this dx(t)/dt = 2 * * F * A * sin (2 * * F * t). This slope has a maximum value of 2**F*A Overload occurs if 2 * * F * A > q * fs To prevent overload we require q * fs > 2 * * F * A Example A = 2 V, F = 3.4 kHz, and the signal is sampled 1,000,000 times per second, requires q > 2 * 3.14 * 3,400 * 2 /1,000,000 V > 42.7 mV Granular noise occurs if the slope changes more slowly than the step size. The reconstructed signal oscillates by 1 step size in every sample. It can be reduced by decreasing the step size. This requires that the sample rate be increased. Delta Modulation requires a sampling rate much higher than twice the bandwidth. It requires oversampling in order to obtain an accurate prediction of the next input, since each encoded sample contains a relatively small amount of information. Delta Modulation requires higher sampling rates than PCM. 5.2 Differential PCM (DPCM) and ADPCM Differentiator Analogue Input Band Limiting Filter + - Quantiser Enoder ADC Encoded Difference Samples Accumulator DAC DPCM is also designed to take advantage of the redundancies in a typical speech waveform. In DPCM the differences between samples are quantized with fewer bits that would be used for quantizing an individual amplitude sample. The sampling rate is often the same as for a comparable PCM system, unlike Delta Modulation. Adaptive Differential Pulse Code Modulation ADPCM is standardised by ITU-T recommendations G.721 and G.726. The method uses 32,000 bits/s per voice channel, as 10 28/06/2016 compared to standard PCM’s 64,000 bits/s. Four bits are used to describe each sample, which represents the difference between two adjacent samples. Sampling is 8,000 times a second. It makes it possible to reduce the bit flow by half while maintaining an acceptable quality. While the use of ADPCM (rather than PCM) is imperceptible to humans, it can significantly reduce the throughput of high speed modems and fax transmissions. The principle of ADPCM is to use our knowledge of the signal in the past time to predict the signal one sample period later, in the future. The predicted signal is then compared with the actual signal. The difference between these is the signal which is sent to line - it is the error in the prediction. However this is not done by making comparisons on the incoming audio signal - the comparisons are done after PCM coding. To implement ADPCM the original (audio) signal is sampled as for PCM to produce a code word. This code word is manipulated to produce the predicted code word for the next sample. The new predicted code word is compared with the code word of the second sample. The result of this comparison is sent to line. Therefore we need to perform PCM before ADPCM. The ADPCM word represents the prediction error of the signal, and has no significance itself. Instead the decoder must be able to predict the voltage of the recovered signal from the previous samples received, and then determine the actual value of the recovered signal from this prediction and the error signal, and then to reconstruct the original waveform. ADPCM is sometimes used by telecom operators to fit two speech channels onto a single 64 kbit/s link. This was very common for transatlantic phone calls via satellite up until a few years ago. Now, nearly all calls use fibre optic channels at 64 kbit/s. 11 28/06/2016